Best prediction in linear models with mixed integer/real unknowns: theory and application

In this contribution, we extend the existing theory of minimum mean squared error prediction (best prediction). This extention is motivated by the desire to be able to deal with models in which the parameter vectors have real-valued and/or integer-valued entries. New classes of predictors are introduced, based on the principle of equivariance. Equivariant prediction is developed for the real-parameter case, the integer-parameter case, and for the mixed integer/real case. The best predictors within these classes are identified, and they are shown to have a better performance than best linear (unbiased) prediction. This holds true for the mean squared error performance, as well as for the error variance performance. We show that, in the context of linear model prediction, best predictors and best estimators come in pairs. We take advantage of this property by also identifying the corresponding best estimators. All of the best equivariant estimators are shown to have a better precision than the best linear unbiased estimator. Although no restrictions are placed on the probability distributions of the random vectors, the Gaussian case is derived separately. The best predictors are also compared with least-squares predictors, in particular with the integer-based least-squares predictor introduced in Teunissen (J Geodesy, in press, 2006).     

Modeling long-period noise in kinematic GPS applications

We develop and test an algorithm for modeling and removing elevation error in kinematic GPS trajectories in the context of a kinematic GPS survey of the salar de Uyuni, Bolivia. Noise in the kinematic trajectory ranges over 15 cm and is highly autocorrelated, resulting in significant contamination of the topographic signal. We solve for a noise model using crossover differences at trajectory intersections as constraints in a least-squares inversion. Validation of the model using multiple realizations of synthetic/simulated noise shows an average decrease in root-mean-square-error (RMSE) by a factor of four. Applying the model to data from the salar de Uyuni survey, we find that crossover differences drop by a factor of eight (from an RMSE of 5.6 to 0.7 cm), and previously obscured topographic features are revealed in a plan view of the corrected trajectory. We believe that this algorithm can be successfully adapted to other survey methods that employ kinematic GPS for positioning.     

The Potential of the Maximum Cross-Correlation Technique to Estimate Surface Currents From Thermal AVHRR Global Area Coverage Data

Having already shown its potential of deriving the vector fields representing the ocean-surface advection from sequential 1.1-km-resolution local area coverage (LAC) Advanced Very High Resolution Radiometer (AVHRR) images, the maximum cross-correlation (MCC) technique here is applied to four 4.4-km-resolution global area coverage (GAC) AVHRR images. The resulting three vector fields are compared to the vector fields obtained from the LAC imagery corresponding to the same satellite passages. To quantify the reduction in accuracy inevitable when applying the method to the lower resolution imagery, the LAC vector fields were assumed to be error free. The deviation of the GAC vectors from the LAC vectors is expressed as percentage errors of the signal variance of meridional u and zonal v velocity components, and they are 16%/30%, respectively, for the best case and 62%/117% and 92%/111% for the other two cases. These results indicate that, in its present state, the GAC data do not allow the MCC technique to extract reliable current-vector information from it     

A community-based urban forest inventory using online mapping services and consumer-grade digital images

Community involvement in gathering and submitting spatially referenced data via web mapping applications has recently been gaining momentum. Urban forest inventory data analyzed by programs such as the i-Tree ECO inventory method is a good candidate for such an approach. In this research, we tested the feasibility of using spatially referenced data gathered and submitted by non-professional individuals through a web application to augment urban forest inventory data. We examined the use of close range photogrammetry solutions of images taken by consumer-grade cameras to extract quantitative metric information such as crown diameter, tree heights and trunk diameters. Several tests were performed to evaluate the accuracy of the photogrammetric solutions and to examine their use in addition to existing aerial image data to supplement or partially substitute for standard i-Tree ECO field measurements.     

Variability analysis of groundwater levels — AGIS-based case study

The present study has analyzed the variability in depth to water level below ground level (bgl) vis-à-vis groundwater development and rainfall from 1987 to 2007 in agriculture dominated Kaithal district of Haryana state in India. Spatial distribution of groundwater depth was mapped and classified into different zones using ILWIS 3.6 GIS tools. Change detection maps were prepared for 1987–1997 and 1997–2007. Groundwater depletion rates during successive decades were compared and critical areas with substantial fall in groundwater levels were identified. Further, block wise trends of change in groundwater levels were also analyzed. The water table in fresh belt areas of the district (Gulha, Pundri and Kaithal blocks) was observed to decline by a magnitude ranging from 10 m to 23 m. In Kalayat and Rajaund blocks, the levels were found fluctuating in a relatively narrow range of 4–9 m. During 1997–2007, the depletion has been faster compared to the preceding decade. Excessive groundwater depletion in major part of the district may be attributed to indiscriminate abstraction for irrigation and decrease in rainfall experienced since 1998. Changes in cropping pattern and irrigation methods are needed in the study area for sustainable management of the resource.     

Assessment of the LandStar Real-Time DGPS Service under Several Operational Conditions

LandStar is a differential global positioning service (DGPS) that provides 24-h real-time positioning for various applications on land, water, and air in North America, Australia, New Zealand, Europe, and Africa. Its focus is on real-time applications requiring a submeter positioning capability such as agriculture, forestry, Geospatial Information Systems (GIS), survey/mapping, and land/vehicular navigation. LandStar uses a Wide Area Network of reference stations to derive DGPS corrections to model the variation of GPS error sources over a large area. These model parameters are used by the Virtual Reference Station processors to calculate standard corrections that are available for all predefined locations in the network. The corrections are transmitted to the user by L-band satellite communication in the standard RTCM SC104 DGPS correction format. This article investigates the performance of the LandStar Mk III system under various operational conditions and assesses its performance in both static and kinematic modes. Four field tests were conducted during 12 months that tested the sysem in clear static and kinematic conditions as well as suboptimal environments associated with low and heavy foliage conditions. Both the accuracy and availability of the system under these conditions is investigated, with an emphasis on whether the above variables are caused by the LandStar system differential corrections, the GPS measurements, or a combination of both. ? 1999 John Wiley & Sons, Inc.     

Habitat analysis for sambar in corbett national park using remote sensing and gis

Habitat analysis for sambar in terms of food, cover, water, space and extent of edge in Corbett National Park using remote sensing and GIS has been attempted. Other physical parameters include climate, topography, fire history, disturbance regimes, weeds etc. IRS-IB LISS II data (FCC, hardcopy) on 1:50.000 scale was interpreted to generate vegetation cover and density map. Other maps showing drainage, water bodies, roads, human habitations and contours were prepared using Survey of India topographical maps. During evaluation of sambar habitat information regarding habitat parameters and their tolerance was collected from existing literature as well as during field observations. Twenty-two transects of one km. length were laid down in all the strata randomly to collect information regarding the structure and composition of the forest and also habitat use (direct and indirect evidences) by sambar. This was then integrated using condition-based equations in the GIS domain to generate suitability maps. Actual sightings on the ground to a large extent supported the results.     

Peculiarities of surface air temperature variations over the Far East regions in 1976–2005

Peculiarities are investigated of the air temperature variation tendencies at some stations of the Far East in 1976–2005. The estimate of linear trend equation coefficients is computed according to the air temperature observation data using the least squares method. It is demonstrated that the air temperature trend in northern regions possesses a small probability at small values of residual variability. In the southern regions, the trend significance increases for almost all seasons at small values of residual variability. At midlatitude stations, the trend significance in January and February decreases considerably due to the large values of residual variability.     

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

The complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is verified through comparison with known semi‐analytical and numerical solutions that involve interaction between a circular opening and specific systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole. Copyright © 2000 John Wiley & Sons, Ltd.